00:01
So we have r of t equals the vector t squared, t to the fourth, t to the sixth.
00:09
All the coordinates are even powers.
00:11
So x equals t squared is greater than are equal to zero.
00:14
So is y equals two to the fourth and z equals t to the six.
00:17
So the whole curve lives in the first octant, which is the positive corner.
00:23
So let's eliminate the parameter.
00:26
So because x equals t squared, y is equal to t to the fourth would be t squared squared squared, which would be x squared, and then z equals t to the six, which is t to the second cubed, which would be then x cubed.
00:43
So the curve lies on the space, the space curve defined by y equals x squared, z equals x cubed where x is greater than equal to zero.
00:53
What this ends up looking like, and i'll do my best, but you would be better suited using a 3d calculator...